The quantitative morphology of linear branched structures in biological tissues is of broad interest. Imaging of these structures provides information concerning the condition of various tissues. For many line-structures, however, quantitative analysis is necessary for rigorous assessment and medical diagnosis. Examples of relevant line-structures include blood vessels, neurons, and retina.
Of particular interest for quantitative analysis are automated two-dimensional (2-D) and three-dimensional (3-D) tracing and morphometry methods for neurons in thick slices of brain tissue. The neurons are imaged by 2-D or 3-D microscopy. Analysis of these images provides traces of dendrites and axons, and produces graph-theoretic or tabular representation of these structures. The analysis captures the essential topological characteristics, providing a number of topological and metric measurements useful in medical evaluation.
The ability to effectively analyze biological tissues depends on the availability of efficient, fast, and robust quantitative techniques that can provide the requisite measurements mentioned above. Currently, most line-structure tracing is conducted by tedious and time-consuming manual tracing. The time and effort required is so large that studies involving large cell sets are precluded. These manual methods typically tolerate low accuracy and suffer from intra- and inter-user inconsistencies.
Some current methods do provide for semi-automatic neuron tracing. In these semi-automatic methods, a human interacts with a microscope enhanced with computer imaging hardware and software. The user performs pattern recognition, and the computer system records the data and generates topological and metric analyses. In some cases, the computer assists the human by automatically aligning a cursor to the nearest image feature or by automatically focusing the microscope. In either case, the operator must trace each neuronal structure manually. A device implementing semi-automatic neuron tracing follows the spatial path of a dendrite after the device is initially set at the proximal part of a dendrite and has been provided with an initial direction of the dendritic path.
The available methods employ various computational approaches. Three approaches have been identified for the analysis of linear branched structures such as neurons and vasculature. One approach is based on skeletonization of the line structure and branch point analysis. A second approach is a chaining method based on enhancing edge and line properties and identifying vessel contours by chaining the edge pixels together. A chaining method usually involves dynamic programming to search for a minimal cost path, Markov chaining, or maximizing the likelihood of a path. Both of these approaches require processing every image pixel with numerous operations per pixel.
Another approach is referred to variously as vectorization, vectorial tracking, or tracing. Vectorization involves first locating an initial point and then exploiting the local image properties to trace the structures recursively. These types of calculations are appropriately termed “exploratory algorithms” as only pixels close to the structures are processed. This approach is particularly relevant when processing speed is crucial, such as in real-time image analysis, or when data sets are very large.
Broadly, three categories of exploratory algorithms or processing techniques are described in the literature. Quantitative coronary angiography (QCA) involves manually entering the initial and end points of a vessel. A tentative centerline might also be entered on occasion. Although these algorithms are very accurate, they are designed to trace vessel segments with no branching or intersection regions and in conditions where speed of calculation is not of great concern.
In a second category, the algorithm starts with a manually entered initial point and an initial direction, and recursively traces the entire arterial tree using a breadth-first search. In the context of neurons, this approach corresponds to tracing a single axon or dendrite tree that is efferent from a single soma. Such methods are not suitable for images containing several neurons with each neuron having several processes efferent from it. The third category includes fully automated methods that tend to overcome the limitations of the first two categories.
Most of the prior work done with vectorization addresses 2-D images or projections of 3-D images. A need remains, however, to extend this work to handle 3-D (volumetric) image space. A related need exists to provide a set of adaptations to handle the imaging artifacts specific to fluorescence confocal microscope images, especially noise, the point-spread function, and discontinuities in structures.